Question 366386
*[invoke plot_any_inequality "x>=0", -10, 10, -10, 10, 300, 300]

*[invoke plot_any_inequality "y>=0", -10, 10, -10, 10, 300, 300]


*[invoke plot_any_inequality "y>=4x-4", -10, 10, -10, 10, 300, 300]


*[invoke plot_any_inequality "y<=x+5", -10, 10, -10, 10, 300, 300]

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Find the intersection of the bounding lines and the axes.
{{{4x-4=0}}}
{{{x=1}}}
({{{1}}},{{{0}}})
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{{{x=0}}}
{{{y=5}}}
({{{0}}},{{{5}}})
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{{{4x-4=x+5}}}
{{{3x=9}}}
{{{x=3}}}
{{{y=x+5=8}}}
({{{3}}},{{{8}}})
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{{{drawing(300,300,-2,8,-2,10,grid(1),circle(0,0,0.3),circle(0,5,0.3),circle(1,0,0.3),circle(3,8,0.3),blue(line(0,5,3,8)),blue(line(3,8,1,0)),graph(300,300,-2,8,-2,10,0))}}}

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The minimum and maximum of your function occurs at one of the vertices.
({{{0}}},{{{0}}}):{{{P=-21x+11y =-21(0)+11(0)=0}}}
({{{0}}},{{{5}}}):{{{P=-21x+11y =-21(0)+11(5)=highlight(55)}}}
({{{1}}},{{{0}}}):{{{P=-21x+11y =-21(1)+11(0)=-21}}}
({{{3}}},{{{8}}}):{{{P=-21x+11y =-21(3)+11(8)=-63+88=25}}}